Why should that be the case? The argument could be also made that since the RNZAF currently lacks an ACF it has already suffered and continues to do so.
For example - do other countries suffer by having an air combat capability? Did we also suffer during the 60 years we maintained combat aircraft and maintained other defence assets?
We can afford to buy and operate an air combat capability without the necessity to borrow billions to do so. Not one cent of the $20B until 2030 will be borrowed unlike other countries which essentially are borrowing billions to support defence industries as part of their industrial - employment policy.
Where we buy our future surface combatants will have a far greater effect on the NZDF Cap Ex budget than operating a squadron of air combat aircraft. That is probably why we will be looking elsewhere in the future in an open competitive process to replace the ANZAC's.
It would come down to funding IMO. If no extra funding is provided for the Personnel and Operating budgets then the NZDF would likely suffer by trying to achieve too much with too little. The CAPEX budget could certainly fund the purchase, but that is only to acquire the aircraft/capability, not sustain or make use of the capability.
From numbers I got looking at the 2015-2016 NZDF annual report (see the NZDF thread) the Operating budget was NZD$737.7 mil. Back when then A-4K Skyhawks were still in service, the ACF had a cost of ~NZD$200 mil. p.a. for operations, personnel, maintenance, etc. I do not know the precise breakdown of the costs, but even with the potential for more efficient operations due to contracting out some functions and keeping the Personnel budget separate, I cannot imagine the Operating budget would now be less than NZD$100 mil. p.a. Given inflation, it could easily be quite a bit higher (like NZD$170+ mil. p.a.) but even NZD$100 mil. would force other Operating activities within the NZDF to be curtailed or outright suspended.
The other alternative would be for the NZDF to attempt to retain all currently existing equipment and capabilities, while adding an ACF back in. However that would likely lead to the under funding of various NZDF kit and capabilities leading to kit decaying, a lack of sufficient training, malfunctions and loss of (or failure to retain) skills. Not to make light of the likely tragic loss of the ARA San Juan, but the condition of the Argentine Air Force, Army, and Navy is what happens when budgeting is inadequate and capabilities are not scaled back. Indeed, the Argentine Air Force still lists the various Mirage aircraft and derivatives as being in the inventory when Argentine news articles from mid-2015 indicate their retirement was imminent and were otherwise limited to daylight VFR operations.
I would really hate to see NZ follow the above model, as it would become a question not of if, but when, there is a failure which results in death or injury to personnel, and damage or loss of kit and infrastructure.